There are few ways to tame this sea giga. Let me explain them all:
1. Just damn battling: Get a fast water mount and literally kite Mosa as you smack its face with your torpor weapon.
2. Trapping: You need to create a trap like a cell. Get a Benemoth dino gateway and a gate, some foundations, and pillars that Mosa can’t go through. Make it follow you into the cage, then get out from the gap that pillars created and shut the door. After that, knock it out and feed it.
3. (and also my favorite) Ammonite Strategy:
Punch an ammonite. It will give you the rage debuff and every creature will chase you down, including the Mosasaurus. So the Mosasaur has a limit on depth. What i mean is that it can’t go higher than a set limit, since it’s a deepsea creature. But when the rage is on, it will ignore the limit and follow you even to shallows. Get out of the water and wait until your rage wears off. The Mosasaur won’t be able to move since it has broken it’s limits and can’t go back. Hit it with your torpor weapon and knock it out.
4. Going Up and Down:
As i mentioned earlier, the Mosasaur has a set limit on depth. Hit the Mosasaur, then let it swim up to you, of course swim away whilst doing that, also hit it while you’re swimming away. After it has reached the limits, it will stop chasing you. When it does, go deeper and hit it again. Go this couple of times until it gets knocked out.
IMPORTANT NOTE: Don’t forget to kill the surrounding creatures like Plesiosaurs, Tusos, Electropus and Anglers since it can attack you and ruin the taming.